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Properties

Label 36992.2.a.bm
Level $36992$
Weight $2$
Character orbit 36992.a
Self dual yes
Analytic conductor $295.383$
Dimension $3$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [36992,2,Mod(1,36992)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("36992.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(36992, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 36992 = 2^{7} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 36992.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,0,2,0,-4,0,6,0,-1,0,4,0,0,0,2,0,0,0,-2,0,6,0,8,0,1,0,2,0,-8, 0,4,0,0,0,-14,0,-4,0,18,0,14,0,-4,0,0,0,6,0,-1,0,0,0,10,0,-22,0,16,0,-4, 0,-12,0,8,0,20,0,-14,0,-10,0,10,0,18,0,-22,0,22,0,0,0,-5,0,-4,0,0,0,-10, 0,-14,0,-2,0,18,0,0,0,14,0,10,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(295.382607157\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 3 q + 2 q^{3} - 4 q^{5} + 6 q^{7} - q^{9} + 4 q^{11} + 2 q^{15} - 2 q^{19} + 6 q^{21} + 8 q^{23} + q^{25} + 2 q^{27} - 8 q^{29} + 4 q^{31} - 14 q^{35} - 4 q^{37} + 18 q^{39} + 14 q^{41} - 4 q^{43} + 6 q^{47}+ \cdots + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.